What AI concept is behind the Mars Exploration Rover (MER)?
The Mars Rover is a highly successful example of the 'New AI' that emerged from work by Rodney Brooks in the 1990s.

In a quote from Brooks: 


  In 1984 I joined the faculty at MIT where I have been ever since. I set up a mobile robot group there and started developing robots that led to the Mars planetary rovers. 


Together with the 'Allen' paper, the foundational AI articles in this area are:


"Elephants don't play chess"
"Intelligence without representation"


Although Brooks initially had difficulty getting this work published, preprints were widely circulated within the AI community. Brook's "Physical Grounding Hypothesis" (essentially: "intelligence requires a body") has now largely supplanted the preceding symbolist approach.

The capabilities of the MARS Rover are organized in a Subsumption Architecture. Rather than maintaining an integrated and complex 'world model', increasingly sophisticated behaviors are stacked in hierarchical layers. For example, 'walking' is a relatively low-level competence, with 'avoiding obstacles' and 'wandering around' being higher-level ones. 



Each layer is represented by a Finite State Machine that reacts to stimuli appropriate to that level. The activity of lower levels can be suppressed ('subsumed') by higher level ones.

Here is a schematic of the bottom two layers of 'Allen', Brook's first subsumption robot: